Warren Currie (https:) Debora Laura
16/05/2022
Warren Currie (https:) Debora Laura
\(\rightarrow\)
We may refer to beliefs supported by data, or which at least do not always contradict data, as theories
We will like theories to have a few other properties such as:
Model: a representation of reality
A structure that:
conceptual (e.g., a statement)
physical (e.g., lab experiment)
mathematical (e.g., ODE)
data-driven (e.g., regression)
computational (e.g., IBM)
“predators can positively impact prey”
Bell & Cuddington 2018
\(\frac{dN}{dt}=f(N,E)+g(N,P,E)\)
\(E(y_i)=β_0+f(x_i)+\epsilon\)
Cuddington & Yodzis 1999
\(\rightarrow\) Model \(\neq\) reality
When constructing a model,one is constantly trading off the degree ofprecision, generality and realism (Levins 1966).It is not possible to include all details of a systemand still have a useful predictive tool. Forexample, a one-to-one scale map of a city mayinclude all details, but ceases to be useful as aguide for finding the nearest hotel. As a result,models are always false in some aspects of theirrepresentation of a system, and there is no onecorrect model that links a theory to a particularsystem (Fig. 1).
\(\rightarrow\) Model \(\neq\) theory
\(\rightarrow\) Theory \(\neq\) Model \(\neq\) theory
while we attempt to make do without it, both of these functions require mechanism
Valle et al. (2009) found that alternate modelingassumptions in the forest stand simulation modelSYMFOR can account for 66–97%of the variancein predicted stand dynamics. While the authorswere able to complete this comparison ofdiffering models formulations for SYMFOR, theynote that it may be very difficult to do the samefor exceedingly complex models.
Because these models arebased on causal mechanisms rather than correla-tion, our confidence in extrapolating beyondknown data is enhanced. Of course, there isalways uncertainty about how an ecologicalprocess will interact with novel global changeconditions.
However, underconditions of global change, models based on thepast behaviour of a system may not be suitablefor projection forward (Williams et al. 2007,Lawler et al. 2010).
Predators negatively impact their prey
how?
fear dynamics?
benefitting competitors
when, always?
is that true for generalist predators and specialists?
what about predators that eat prey competitors?
what about predators that modify the environment?
Without mechanism, we can’t answer these questions, and that’s a problem, since if we get the answer wrong, we might take an action that has the opposite of the desired effect
starting from \(\frac{dN}{dt}=f(N)-g(N,P)\) is no different than starting from \(y_i=\beta_0 + f(x_i)+\epsilon\) in terms of mechanism
mechanism requires an explanation or idea about the predators negatively impact net prey population growth rate (what is g(N, P)?)
-actually, I exaggerate, there’s a little bit of something here, that is not obvious in the statistical model, we require g(N,P) is large or similar to f(N) to see a negative impact
-we can leave g(N,P) to be a mere description of phenomena, or we can examine natural data closely, devise experiments, or reason logically to develop ideas about mechanism (e.g., Holling REF)
once the function is specificed, the model can also suggest expected behaviour for given conditions within the domain of application (this is a two-species model!, well it might work okay for agricultural fields), or to make guesses outside of this domain (true, but the interaction strength between these two species is really large compared to everything else)
one advantage tho, the model can include a variety of functional forms that pertain to different mechanisms… we have to stop forgetting this!!
i.e., Lotka-Volterra pred-prey model (\(\frac{dN}{dt}=rN-aNP\)), Rosenzweig-McArthur pred-prey model (\(\frac{dN}{dt}=rN(1-\frac{N}{K})-\frac{aNP}{N+N_0}\))
-yes, these model are false
more generally, mathematical models often tend to appeal to classifications of species interactions, a platonic ideal if you will, which more or may not exist e.g., a “predator-prey” model
these models have dubious explanatory value outside of the examplar classification system,
“predator-prey” model supposes there is a class of predator-prey interactions that have general properities accross species, systems and time that are related to the outcome of the interaction (-/+)
as I will discuss, the net effect of pairwise species interactions is not fixed.
Nor indeed is the a fixed net effect of the interaction of a species with its environment or community etc,
\(\leftarrow\) this is the first reason I don’t think this is a helpful approaoch missing from machine learning approaches, their oversimplified assumptions and extremely specific nature prohibit the universal predictions achievable by machine learning.” Baker et al. (2018). Mechanistic models versus machine learning, a fight worth fighting for the biological community? Biology Letters, 14(5), 20170660. https://doi.org/10.1098/rsbl.2017.0660
Any attempt by machine learning technologies to predict individual patient outcomes from past observations using a patient database is potentially able to identify which of existing treatments is most adequate, but intrinsically unable to suggest new treatment protocols or to provide accurate predictions for new treatments. In the literature, this aspect is referred as the ‘inductive capability’ of the learning algorithms (from past data, one can identify patterns happening in the data). This is vastly different from the deductive capability of mechanistic models, in which the combination of logical (mechanistic) principles enables extrapolation to predictions about behaviours not present in the original data [4]. In short, mechanistic models can provide insights and understanding into the mechanistic functions of treatments, and these are necessary to overcome the limitations of machine learning predictions
I haven’t seen an example of “universal predictions achievable by machine learning” in ecology but I am certainly of the mind that both approaches are useful IN THEIR DOMAIN OF APPLICATION
“While mechanistic models provide the causality
(e.g., invasive rusty crayfish eat endangered Hine’s emerald dragonfly larvae)
Entropy: the model is calibrated to find the distribution that is most spread out, or closest to uniform throughout the study region.
Constraints: the rules that constrain the predicted distribution. These rules are based on the values of the environmental variables (called features) of the locations where the species has been observed.
use experimental data to suggest candidate predictors: may require cold stratification, refer moist sites
intial Maxent model to find strong candidates and eliminate correlated predictors (normally we would leave these in and assume that the penalization would takec are of correlation)
Bay of Quinte before and after mussel invasion
“In the mid-1990s, zebra and quagga mussels (Dreissena spp.) invaded the area, dramatically changing the water clarity because of the filter-feeding capacity.”
Bay of Quinte remedial action plant (2017)
-asymptotic vs transient dynamics predicted by models
-long transients can be a quite common prediction
all of which arise from the SAME mechanistic model
-often mathematical, but need not be so.
Environmental stochasticity or varia- tion in parameter values might lead to amplification of disturbances [24] or differences in expected dynamics. For example, varying parameter values in a differential equation model can determine whether a monotonic or oscillating approach to a stable equilibrium is expected (Box 1). There- fore, uncertainty in parameter values will lead to uncertainty about which dynamic behaviors are most likely.
We thank Luwen Chang and Matthew Zhou for their amazing learning curves, and subsequent help coding up the modules. The eCampusOntario grant also funded several students to evaluate an early version of the materials. Lina Aragon Baquero, Lauren Banks, Madison Brook, Jacob Burbank, Nicole Gauvreau and Aranksha Dilip Thakor provided valuable feedback.
The Git and GitHub module builds upon workshop materials that were originally developed with Chris Grandin (DFO), who AME also thanks for assistance with the module.
The Quantitative Biology in Life Science Graduate Programs workshop from which this work arose which was supported by funding from the Burroughs Wellcome Fund, from National Science Foundation Award DBI-1300426 for NIMBioS, with additional support from the University of Tennessee. The Workshop arose from a partnership between NIMBioS and the Southeast Center for Mathematics and Biology (SCMB).
Support for the development of online training materials comes from the Government of Ontario through a grant from eCampusOntario, and the support of Fisheries and Oceans Canada and the Faculty of Science, University of Waterloo (https://www.quantitative-biology.ca)
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